DoorDash Inc. is close to securing new funding that would value the largest U.S. meal-delivery company at more than $15 billion before the infusion, as a wave of deal making sweeps over the red-hot industry.

The closely held company plans to sell hundreds of millions of dollars of equity to existing backer T. Rowe Price Group Inc. as well as Fidelity Investments and others, according to people familiar with the matter.

The…

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